In this section we test which variables it is beneficial to lock to some value, given a (fixed) standard deviation on the catch. For these experiments we use a fixed standard deviation of 0.15 for the catch. For all the experiments this data set is used.

The variables in question are the catchability, standard deviation of the survey indices, and the mortality. For comparison, we first run the model without latent variables, and then with all three variable locked. Both of these experiments are conducted in the section on choosing the standard deviation as well.

If either q or M are fixed, then the results are similar to those of the case with no latent variables, but with much smaller confidence intervals, and better fit with the survey observations.

If neither of these two variables are fixed, the results are worse than with no latent variables, in the sense that the confidence intervals are larger, and that the mortality often reaches its upper bound. The misfit with the survey observations is also worse in this case.

Detailed comments:

Experiment

Comments

Exact catch (no latent variables)

This we will refer to as the base case. The parameter estimates are seemingly reasonable, but the confidence intervals are relatively large. The parameter estimates and standard deviations are:

The N0 variables are (despite their name) billions of individuals in age group three, with the first cohort born in 1991, the next in 1992, and so on.

All variables locked

The only free variables are the stock sizes and the latent variables. The stock size estimates are essentially equal to the base case. Since so many variables are locked, the confidence intervals are very small. The misfit is better than for the base case.

No variables locked

BAD. The stock estimates are about double what they are in the base case. To compensate, the mortality almost reaches its upper bound, and the confidence intervals are larger than for the base case. The misfit is worse than for the base case.

q locked

GOOD The stock estimates are slightly larger than for the base case. The mortality is also slightly larger, whereas the standard deviation of the survey observations is about the same. The confidence intervals are very small, and the misfit is better than for the base case.

s locked

BAD The stock sizes once again grow to about twice of those of the base case. The mortality reaches its upper bound, and the catchability q is much lower than for the base case. The misfit is worsened.

M locked

GOOD The estimates are more or less the same as for the base case, but the confidence intervals are much smaller. The misfit is improved.